Transfer coefficient relation

A list of mass transfer coefficient relations provided in Table 4.2 illustrates the types of experimentally determined relations that exist. They are typically of the form of equation (E4.5.4), although some deviations occur due to a theoretical analysis of mass transfer. Theoretical and experimental analyses have shown that Sh for an interface that acts like a fluid and Sh for an interface that acts like a solid. 

VOCs), and to a decrease in production yields. Quantitation of these phenomena and determination of material balances and conversion yields remain the bases for process analysis and optimisation. Two kinds of parameters are required. The first is of thermodynamic nature, i.e. phase equilibrium, which requires the vapour pressure of each pure compound involved in the system, and its activity. The second is mass-transfer coefficients related to exchanges between all phases (gas and liquids) existing in the reaction process. 

In expression (3.37), jo is the exchange current density, u and a2 are the transfer coefficients related to, respectively, the forward and backward reaction, n is the number of electrons transferred per reaction, and t]aot is the activation loss. 

Describe the physical mechanism of convection. How is the convection heat-transfer coefficient related to this mechanism ... 

A comparison of the heal transfer coefficient relations for a vertical tube of height L and a horizontal tube of diameter D yields... 

Note that Fq. 10-33 can be obtained from the heat transfer coefficient relation for a horizontal tube by replacing D in that relation by ND. This relation docs not account for the increase in heat transfer due to the ripple formation and turbulence caused during drainage, and thus generally yields conservative results. 

The oveiall heat transfer coefficient relation given above is valid for clean surfaces and needs to be modified to account for the effects of fouling on both the inner and the outer surfaces of the tube. For an uofinned shell-and-tube heat exchanger, it can be expressed as... 

With the matrix of low flux mass transfer coefficients related to the matrix of Stanton numbers by Eq. 10.4.25 we may write... 

An analogue heat transfer coefficient relation has been derived by the penetration concept. The heat transfer theory is reviewed by Thomson [153]. 

The tube-side heat transfer coefficient related to tube outside diameter is h = bcF where is a correction factor for h. 

The overall heat-transfer coefficient, related to the instantaneous total area of the rising two-phase drop, increases sharply with evaporation up to 3-10 wt-% vapor content, depending on the system and conditions, and then decreases quite moderately until evaporation is complete. Thus it indicates the decreasing effect of the internal resistance to heat transfer in the first stages of the evaporation process, and the moderate decrease in the relative transfer area in the subsequent stages of the process (SI2). The instantaneous overall heat-transfer coefficients are 200-400 Btu/hr/ft /°F for D =3.5 mm, and 500-700 Btu/hr/ft /°F for Z> = 2.0 mm. 

Also included in Fig. 23 are Bonilla s data (B9a) for nucleate boiling of pentane from a chrome-plated heater, as well as the average over all heat-transfer coefficient, related to the instantaneous overall heat-transfer area, for pentane drops evaporating while rising in water. As noted earlier, the heat-transfer coefficient in the latter case was found to be practically independent of the temperature driving-force in the range studied (up to 15°C). 

The overall transfer coefficients (related to the overall transfer area) obtained in this three-phase two-component condensation study were about 600 and 1100 Btu/hr/ft /°F for the large and small bubbles, respectively. These compare favorably with the values reported for condensation of steam in water, which are, however, one order of magnitude larger. The difference is reasonable in view of the possibility for mass diffusion at the gas-liquid interface in the two-phase steam-water system, as well as the much higher turbulence encountered, especially in Bankoff s system (B2). 

Overall transfer coefficient, related to average of instantaneous area 0 Overall transfer coefficient, related to initial drop area... 

A surface heat transfer coefficient h can be defined as the quantity of heat flowing per unit time normal to the surface across unit area of the interface with unit temperature difference across the interface. When there is no resistance to heat flow across the interface, h is infinite. The heat transfer coefficient can be compared with the conductivity the conductivity relates the heat flux to the temperature gradient the surface heat transfer coefficient relates the heat flux to a temperature difference across an unknowm distance. Some theoretical work has been done on this subject [8], but since it is rarely possible to achieve in practice the boundary conditions assumed in the mathematical formulation, it is better to regard it as an empirical factor to be determined experimentally. Some typical values are given in Table 2. Cuthbert [9] has suggested that values greater than about 6000 W/m K can be regarded as infinite. The spread of values in the Table is caused by mold pressure and by different fluid velocities. Heat loss by natural convection also depends on whether the sample is vertical or horizontal. Hall et al. [10] have discussed the effect of a finite heat transfer coefficient on thermal conductivity measurement. 

Introducing an overall mass transfer coefficient / ]] related to the overall mass transfer resistance in phase II, it follows that... 

The variety of regimes during the forced convection boiling in tubes or ducts requires different correlations in order to determine the heat transfer coefficient related to the respective boiling mechanisms. The well-established correlations have been developed for nucleate boiling controlled heat transfer - when evaporation occurs at the inner tube surface - and convective boiling heat transfer - when evaporation occurs at the liquid film interface. 

Equimolar counterdiffusion Diffusion of i through stagnant s Units of transfer coefficient Relation between the two transfer coefficients... 

How is a mass transfer coefficient related to a reaction rate constant ... 

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